[NOI2007 Day1] 货币兑换 Cash

vijos P1508 / BZOJ 1492

膜拜了这么久的cdq分治，终于有机会亲自来写了。虽然这个思想很好理解，先做前一半，计算前一半对后一半的影响，再做后一半。但是由于我这个傻Ⅹ，以前既没有做过斜率优化，也没有做过维护凸包之类，花了好久时间捣鼓具体做法，而且理解思路后写起来还是有点难度的。

主要网上的解题各有各的思路，有的是F数组存最多多少B券，有的是存最多多少A券，虽然大同小异，但是一开始我没意识到所以orz了。

参考资料：

《从Cash谈一类分治算法的应用》——cdq

《cdq分治相关》

同时，我也很大程度上参考了这里的代码。=v=好不容易找了一个易读的C++代码…差不多就是翻译了过来，我的程序里写了“//？”是修改过的。

这么神的题一定要好好温习，同时也要好好学splay啊，至今没有成功码过一次QAQ

program cash;
//orz cdq
const eps=0.000000001;
      maxn=100010;
type typeq=record
             k,a,b,r:real;
             pos:longint;
           end;
     typep=record
             x,y:real;
           end;
var i,j,n,s:longint;
    //a,b,r:array[1..100000] of longint;
    f:array[0..maxn] of real;
    q,nq:array[1..maxn] of typeq;
    p,np:array[1..maxn] of typep;
    st:array[1..maxn] of longint;
function max(a,b:real):real;
begin
  if a>b then exit(a) else exit(b);
end;

procedure qsort(l,r:longint);
var i,j:longint;
    mid:real;
    temp:typeq;
begin
  i:=l;j:=r;mid:=q[(l+r) div 2].k;
  while i<=j do
    begin
      while q[i].k<mid do inc(i);
      while q[j].k>mid do dec(j);
      if i<=j then
        begin
          temp:=q[i];q[i]:=q[j];q[j]:=temp;
          inc(i);dec(j);
        end;
    end;
  if i<r then qsort(i,r);
  if j>l then qsort(l,j);
end;

function getk(a,b:longint):real;
begin
  if a=0 then exit(-maxlongint+1);
  if b=0 then exit(maxlongint);
  if (p[a].x-p[b].x<=eps) and (p[a].x-p[b].x>=-eps) then exit(-maxlongint+1);
  exit((p[a].y-p[b].y)/(p[a].x-p[b].x));
end;

procedure solve(l,r:longint);
var mid,l1,l2,top,i,j:longint;
begin
  if l=r then
    begin
      f[l]:=max(f[l-1],f[l]);
      p[l].y:=f[l]/(q[l].a*q[l].r+q[l].b);
      p[l].x:=p[l].y*q[l].r;
      exit;
    end;
  mid:=(l+r) div 2;l1:=l;l2:=mid+1;
  for i:=l to r do
    if q[i].pos<=mid then
      begin
        nq[l1]:=q[i];inc(l1);  //?
      end
    else
      begin
        nq[l2]:=q[i];inc(l2);  //?
      end;
  for i:=l to r do q[i]:=nq[i];
  solve(l,mid);
  top:=0;
  for i:=l to mid do
    begin
      while (top>=2) and (getk(i,st[top])+eps>getk(st[top],st[top-1])) do dec(top);
      inc(top);st[top]:=i;
    end;
  j:=1;
  for i:=r downto mid+1 do  //update
    begin
      while (j<top) and (q[i].k<getk(st[j],st[j+1])+eps) do inc(j);
      f[q[i].pos]:=max(f[q[i].pos],p[st[j]].x*q[i].a+p[st[j]].y*q[i].b);
    end;
  solve(mid+1,r);
  l1:=l;l2:=mid+1;
  for i:=l to r do      //?
    if ((p[l1].x<p[l2].x) or (l2>r)) and (l1<=mid) then
      begin
        np[i]:=p[l1];inc(l1);
      end
    else
      begin
        np[i]:=p[l2];inc(l2);
      end;
  for i:=l to r do
    p[i]:=np[i];
end;

begin{main}
  readln(n,f[0]);
  for i:=1 to n do
    begin
      readln(q[i].a,q[i].b,q[i].r);
      q[i].k:=-q[i].a/q[i].b;
      q[i].pos:=i;
    end;
  qsort(1,n); //sort array q[i].k
  solve(1,n); //cdq solve
  writeln(f[n]:0:3);
end.

测试数据 #0: Accepted, time = 0 ms, mem = 12876 KiB, score = 10

测试数据 #1: Accepted, time = 0 ms, mem = 12876 KiB, score = 10

测试数据 #2: Accepted, time = 0 ms, mem = 12876 KiB, score = 10

测试数据 #3: Accepted, time = 0 ms, mem = 12876 KiB, score = 10

测试数据 #4: Accepted, time = 0 ms, mem = 12876 KiB, score = 10

测试数据 #5: Accepted, time = 15 ms, mem = 12876 KiB, score = 10

测试数据 #6: Accepted, time = 296 ms, mem = 12880 KiB, score = 10

测试数据 #7: Accepted, time = 312 ms, mem = 12880 KiB, score = 10

测试数据 #8: Accepted, time = 578 ms, mem = 12876 KiB, score = 10

测试数据 #9: Accepted, time = 609 ms, mem = 12876 KiB, score = 10

Accepted, time = 1810 ms, mem = 12880 KiB, score = 100